Primality proof for n = 1002328039319:
Take b = 2.
b^(n-1) mod n = 1.
3969899 is prime. b^((n-1)/3969899)-1 mod n = 221842812586, which is a unit, inverse 718861591819.
(3969899) divides n-1.
(3969899)^2 > n.
n is prime by Pocklington's theorem.